To prevent the occurrence of rapid roll of a car body, to increase only a spring constant in a microamplitude displacement region acting in a transient state of unsprung damping and revolution, to improve driving stability without widely reducing a riding feeling and to improve driving stability under various states during running by increasing only a spring constant at the initial stage of operation in an arbitrary stroke (position).

The interior of a cylinder 2 is partitioned into upper and lower chambers A and B by a piston 5 mounted on the lower end tongue groove part of a piston rod 1 and meanwhile, the piston rod is stretchably guided by the piston, a rod guide 14 fitted in a cylinder upper end, and a seal 6 to cut off outside air. In a so formed hydraulic shock absorber, a lip spring 12 non-movably fastened directly or indirectly through a spring against the rod guide 14 or slidably fitted in a piston rod 1 is mounted thereon.